There are essentially two prior art methodologies, “indirect” and “direct”, for measuring optical forces acting on a trapped microscopic sample. The indirect methods generally have in common the use of a single-beam laser which require the use of complex mathematical models of the trap (harmonic potential) and of the environment (fluid with a homogeneous index of refraction and viscosity, under low Reynolds number conditions) to determine forces acting on a sample that must be spherical in form. The method of indirectly measuring forces on a trapped sample is disclosed in Svoboda, K. & Block, S. M. “Biological Applications of Optical Forces”, Annual Review of Biophysics and Biomolecular Structure Vol. 23, pp. 247-285 (1994) and references therein and also in the patent J. Finer, R. Simmons, J. Spudich and S. Chu, “Optical trap system and method”, U.S. Pat. No. 5,512,745 (1996). Also, the theory behind the measurement method is disclosed in Gittes, F. & Schmidt, C. F. “Interference model for back-focal-plane displacement detection in optical tweezers”, Optics Letters Vol. 23, pp. 7-9 (1998) and a calibration procedure for determining the stiffness constant of the optical trap in K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers”, Review of Scientific Instruments Vol. 75, pp. 594-612 (2004).
The “indirect” single-beam systems have many inadequacies. For example, the measurements depend on many experimental variables that change from experiment to experiment (e.g., temperature, relative index of refraction between sample and medium, size of samples, laser power, numerical aperture of the objective, etc.). In practice, it is necessary to recalibrate these systems each time they are used. This is a complex procedure that requires specialized equipment (piezo actuators) and human expertise which make the systems impractical for commercial use. There are a number of other problems associated with the “indirect” single-beam methods. First, it is not possible to measure forces on non-spherical samples. They require the use of microsphere “handles”. Second, it is not possible to make measurements with non-gaussian laser beams because these do not produce harmonic potentials. This leaves aside beams with interesting characteristics such as the periodic potentials used in optical sorting or the Bessel and Laguerre-Gauss beams, which induce rotations. Third, it is not possible to make measurements in non-homogeneous media, which limits the feasible experiments essentially to those performed in vitro. An important example is experiments inside living cells, which are not possible since the optical properties of the cytosol change from point to point. The cell has to be recreated in a simplified form. In fact, part of the merit of an experiment with optical tweezers in the cellular domain consists of the ability to overcome this difficulty.
The prior art “direct” methods for measuring optical forces on a trapped force require the use of two counter-propagating laser beams. This method has been disclosed in U.S. Pat. No. 7,133,132 (Bustamante et al.) and in two preceding articles entitled “Overstretching B-DNA: The Elastic Response of Individual Double-Stranded and Single-Stranded DNA Molecules”, Science, Vol. 271, pp. 795-799 (1996) and “Optical-Trap Force Transducer That Operates by Direct Measurement of Light Momentum”, Methods of Enzymology, Vol. 361, pp.134-162 (2003). The method has also been described by Grange et al. in an article entitled “Optical tweezers system measuring the change in light momentum flux”, Review of Scientific Instruments, Vol. 23, No. 6, pp. 2308-2316 (2002) and in S. Smith doctoral thesis: “Stretch Transitions Observed in Single Biopolymer Molecules (DNA or Protein) using Laser Tweezers”, University of Twente, The Netherlands (1998).
The prior art “direct” methods for measuring optical forces acting on a trapped sample do so by measuring the force directly by means of momentum changes. These prior art traps are based on dual counter-propagating beams which require duplicated and specific optical setups (two lasers, two telescopes, two microscope objectives, two PSD detectors, etc.) which make them infeasible for integration within the optical trains of commercial microscopes and currently available optical tweezer systems.
Moreover, the use of duplicated optical components makes these systems expensive and more difficult to operate. An important point is that the opinion among those skilled in the art is that the use of single-beam traps for measuring forces using the “direct” method is impossible. Bustamante et al., proclaims so on page 140 in the article entitled “Optical-Trap Force Transducer That Operates by Direct Measurement of Light Momentum” discussed above. Neuman et al. proclaims the same on page 2802 in the article “Optical trapping (review article)”, Review of Scientific Instruments, 75, 2787-2809 (2004). Williams opines the same on page 5 of the thesis entitled “Optical Tweezers: Measuring Piconewton Forces”. Also, Grange et al. in the article entitled “Optical tweezers system measuring the change in light momentum flux” observes the same in page 2308 and S. Smith in his PhD thesis “Stretch Transitions Observed in Single Biopolymer Molecules (DNA or Protein) using Laser Tweezers” is of that same opinion in page 17.
A reason for this opinion is that those skilled in the art believe that a single beam trap would require a narrow cone of light if that cone of light is to be captured (for analysis) by a collecting lens despite the deflection induced by the sample. They believe that if a high numerical aperture lens is used instead, the outermost exiting rays could not be collected by the analysing lens. That required narrowness of the cone of light is insufficient to trap objects since the scattering force due to reflected light would overcome the axial gradient (trapping) force To avoid the dilemma a counter-propagating lens design is used to create the traps at the expense of a higher experimental complexity.
What is needed is a simplified system and method for measuring optical forces acting on a trapped sample which solves the aforementioned problems.